Exponential sums of the M\"{o}bius function and flat polynomials

Abstract

We present an elementary problem on analytic polynomials with coefficients $\pm 1$ or in $\{0,\pm 1 \}$ which implies Riemann hypothesis. It is turns out that this problem is a particular case of the weak form of a flat polynomials problem asked by Erd\"os in his 1957's paper. We provide also under an extra-condition the converse.